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3 years ago

7

Rhett is solving the quadratic equation 0= x2 – 2x – 3 using the quadratic formula. Which shows the correct substitution of the

values a, b, and c into the quadratic formula?

1 answer:

lesya692 [45]3 years ago

4 0

Answer:

The correct option is 1.

Step-by-step explanation:

If a quadratic equation is defined as

$ax^2+bx+c=0$

then the quadratic formula is

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

The given equation is

$0=x^2-2x-3$

Here, a=1, b=-2 and c=-3.

Substitute these values in the above formula.

$x=\frac{-(-2)\pm \sqrt{(-2)^2-4(1)(-3)}}{2(1)}$

$x=\frac{2\pm \sqrt{(-2)^2-4(1)(-3)}}{2(1)}$

Therefore, the correct option is 1.

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What is the distance between (-2 1/2, -3) and (1, -3)

Igoryamba

Answer:

D

Step-by-step explanation:

(-2 1/2, -3) = (-5/2 , -3) & (1, -3)

$Distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\\\ =\sqrt{(1-[\frac{-5}{2}])^{2}+(-3-[-3])^{2}}\\\\ =\sqrt{(1+\frac{5}{2})^{2}+(-3+3)^{2}}\\\\ =\sqrt{(\frac{7}{2})^{2}} \\\\=\frac{7}{2}\\\\=3\frac{1}{2}$

4 0

3 years ago

Read 2 more answers

The question is :

vovikov84 [41]

You are correct, the profit is modeled by:
-0.1t² + 6t + 67

We are also told that "t" is the number of years after 2010. So in 2016, the value of t will be 6. We substitute this into the equation we formed:

-0.1(6²) + 6(6) + 67
= 106.6 thousand dollars

3 0

3 years ago

I’m slow and lazy and yeah sorry just at least help

Anna007 [38]

Answer:

2) x = 6 y = 7 3) x = -5 y= 2

Step-by-step explanation:

2) 10x - 8y = 4

2(-5x + 3y = -9)

-10x + 6y = -18

10x - 8y = 4 Add both equations together

-2y = -14

y = 7 Divide both sides by -2

10(x) - 8(7) = 4 Plug in 7 for the y to solve for x

10x - 56 = 4

+ 56 + 56 Add 56 to both sides

10x = 60

x = 6 Divide both sides by 10

3) Where the two lines intersect, that is the solution to x and y.

The lines intersect at (-5,2). x = -5 y = 2

3 0

3 years ago

Calculate two iterations of Newton's Method for the function using the given initial guess. (Round your answers to four decimal

pickupchik [31]

Answer:

The first and second iteration of Newton's Method are 3 and $\frac{11}{6}$ .

Step-by-step explanation:

The Newton's Method is a multi-step numerical method for continuous diffentiable function of the form $f(x) = 0$ based on the following formula:

$x_{i+1} = x_{i} -\frac{f(x_{i})}{f'(x_{i})}$

Where:

$x_{i}$ - i-th Approximation, dimensionless.

$x_{i+1}$ - (i+1)-th Approximation, dimensionless.

$f(x_{i})$ - Function evaluated at i-th Approximation, dimensionless.

$f'(x_{i})$ - First derivative evaluated at (i+1)-th Approximation, dimensionless.

Let be $f(x) = x^{2}-8$ and $f'(x) = 2\cdot x$ , the resultant expression is:

$x_{i+1} = x_{i} -\frac{x_{i}^{2}-8}{2\cdot x_{i}}$

First iteration: ( $x_{1} = 2$ )

$x_{2} = 2-\frac{2^{2}-8}{2\cdot (2)}$

$x_{2} = 2 + \frac{4}{4}$

$x_{2} = 3$

Second iteration: ( $x_{2} = 3$ )

$x_{3} = 3-\frac{3^{2}-8}{2\cdot (3)}$

$x_{3} = 2 - \frac{1}{6}$

$x_{3} = \frac{11}{6}$

7 0

3 years ago

If 541 people use the swimming pool and children pay 1.75 dollars and adults pay 2.25 and in total earned was 1041.25 how many c

Zina [86]

Answer:

352 children

Step-by-step explanation:

Solve algebraically using a system of equations

Assign variables

let "a" be the number of adults

let "c" be the number of children <-- We want to find this

a + c = 541 Equation for number of people

2.25a + 1.75c = 1041.25 Equation for money

<u>Rearrange the equation for people</u>. Isolate the variable you don't want to find.

a = 541 - c

<u>Substitute</u> "541 - c", replacing "a", in the equation for money

2.25a + 1.75c = 1041.25

2.25(541 - c) + 1.75c = 1041.25 Distribute over brackets

1217.25 - 2.25c + 1.75c = 1041.25 Collect like terms

1217.25 - 0.5c = 1041.25 Simplified equation

<u>Start isolating "c".</u> Move anything that's not "c" to the right side. Move numbers in reverse BEDMAS order. That means we will add/subtract before dividng/multiplying. When moving a number, do its reverse operation to the entire equation.

1217.25 - 0.5c = 1041.25 Do the reverse of positive 1217.25

1217.25 - 1217.25 - 0.5c = 1041.25 - 1217.25 Subtract 1217.25 on both sides

-0.5c = -176 Do the reverse of multiplying by -0.5

-0.5c/-0.5 = -176/-0.5 Divide both sides by -0.5

c = 352 Number of children

Therefore, there were 352 children in the pool.

5 0

3 years ago